Meanwhile, melt remaining 4 Tbsp. butter in a medium saucepan over medium-low heat. Add flour and cook, stirring constantly, until foamy and nutty smelling, 1–2 minutes. Whisking constantly, gradually add milk and bring to a simmer. Cook, whisking often, until mixture coats the back of a spoon, about 3 minutes. Stir in 1/3 cup Parmesan and 1/3 cup Pecorino; season with 1/2 tsp. salt and remaining 1/4 tsp. pepper.